In this thesis, a detailed description of acoustic cloaking is put forth using a coating consisting of discrete layers, enabling the cancellation of the scattered field around the object. This particular approach has previously only been applied to electromagnetic waves, for which it was observed that cloaking could be achieved using isotropic materials over a finite bandwidth. The analysis begins with a presentation of the theoretical formulation, which is developed using classical scattering theory for the scattered acoustic field of an isotropic sphere coated with multiple layers. Unlike previous works on acoustic scattering from spherical bodies, the criteria for acoustic cloaking is that the scattered field in the surrounding medium be equal to zero, and seeking a solution for the layer properties which achieve this condition.
To effectively investigate this situation, approximate solutions are obtained by assuming either quasi-static limits or thin shells, which provide valuable insight into the fundamental nature of the scattering cancellation. In addition, using these approximate solutions as a guide, exact numerical solutions can be obtained, enabling the full dynamics of the parameter space to be evaluated. Based on this analysis, two distinct types of acoustic cloaking were found: a plasmonic cloak and an anti-resonance cloak.
The plasmonic cloak is a non-resonant type of cloak, named plasmonic because of its analogous behavior to the non-resonant cloak observed in electromagnetic waves which utilizes plasmonic materials to achieve the necessary properties. Due to the non-resonant behavior, this type of cloak offers the possibility of a much broader range of cloaking. To expand this design beyond wavelengths on the order of the uncloaked scatterer, multilayered cloak designs are investigated.
The anti-resonance cloak, as the name suggests, uses the anti-resonances of the modes within the cloaking layer to supplement the non-resonant plasmonic cloaking of the scattered field. Although somewhat more limited in bandwidth due to the presence of anti-resonances (and the accompanying resonances), this type of cloak enables a larger reduction in the scattering strength, compared with using a single elastic layer utilizing only non-resonant cloaking. A thorough investigation of the design space for a single isotropic elastic cloaking layer is performed, and the necessary elastic properties are discussed.
The work in this thesis describes the investigation of the theoretical formulation for acoustic cloaking, expanding upon the use of scattering cancellation previously developed for the cloaking of electromagnetic waves. This work includes a detailed look at the different physical phenomena, including both resonant and non-resonant mechanisms, that can be used to achieve the necessary scattering cancellation and which can be applied to a wide range of scattering configurations for which cloaking would be desirable. In addition to laying out a broad theoretical foundation, the use of limiting cases and practical examples demonstrates the effectiveness and feasibility of such an approach to the acoustic cloaking of a spherical object.